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- W3048180864 abstract "We prove a sharp lower bound for the Tanaka-Webster holomorphic sectional curvature of strictly pseudoconvex real hypersurfaces that are semi-isometrically immersed in a Kahler manifold of nonnegative holomorphic sectional curvature under an appropriate convexity condition. This gives a partial answer to a question posed by Chanillo, Chiu, and Yang regarding the positivity of the Tanaka-Webster scalar curvature of the boundary of a strictly domain in $mathbb{C}^2$ from 2012. In fact, the main result proves a stronger positivity property, namely the $frac12$-positivity in the sense of Cao, Chang, and Chen, for compact convex real hypersurfaces in a Kahler manifold of nonnegative holomorphic sectional curvature. Our approach is rather simple and uses a version of the Gauss equation for semi-isometric CR immersions of pseudohermitian manifolds into Kahler manifolds." @default.
- W3048180864 created "2020-08-13" @default.
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- W3048180864 date "2020-08-10" @default.
- W3048180864 modified "2023-09-27" @default.
- W3048180864 title "The holomorphic sectional curvature and convex real hypersurfaces in Kahler manifolds." @default.
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